# How do you simplify Square root of 24 + Square root of 54?

## $\sqrt{24} + \sqrt{54}$

Jun 17, 2018

$5 \sqrt{6}$

#### Explanation:

As a first step you are looking for squared values that you can 'take outside' the roots. Then seeing what you can do with the remaining roots.

$24 = 4 \times 6 = {2}^{2} \times 6$
$54 = 2 \times 27 = 2 \times 3 \times 9 = 6 \times {3}^{2}$

Putting this together we have:

$\sqrt{24} + \sqrt{56} = \sqrt{{2}^{2} \times 6} + \sqrt{{3}^{2} \times 6}$

$\textcolor{w h i t e}{\text{dddddddddddddd") 2sqrt(6)color(white)("d")+color(white)("d}} 3 \sqrt{6}$

$\textcolor{w h i t e}{\text{ddddddddddddddd}} \sqrt{6} \left(2 + 3\right) = 5 \sqrt{6}$

Jun 17, 2018

sqrt(24)+sqrt(54)=color(blue)(5sqrt(6)

#### Explanation:

$\textcolor{\lim e}{\sqrt{24}} + \textcolor{m a \ge n t a}{\sqrt{54}}$

$\textcolor{w h i t e}{\text{XXX}} = \textcolor{\lim e}{\sqrt{{2}^{2} \cdot 6}} + \textcolor{m a \ge n t a}{\sqrt{{3}^{2} \cdot 6}}$

$\textcolor{w h i t e}{\text{XXX}} = \textcolor{\lim e}{2 \sqrt{6}} + \textcolor{m a \ge n t a}{3 \sqrt{6}}$

$\textcolor{w h i t e}{\text{XXX}} = \textcolor{b l u e}{5 \sqrt{6}}$